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NEUMANN, John von. On an Algebraic Generalization of the Quantum Mechanical Formalism (Part I). Offprint from: Recueil Mathématique. Moscow, 1936. 8 o. Original printed wrappers (rebacked, corners and edges repaired); cloth folding case. Provenance : John von Neumann (with autograph notations in some margins). FIRST EDITION, offprint issue. Von Neumann's paper, published in a Russian mathematical journal, continues his axiomatization of quantum mechanics, his most famous work in theoretical physics. "When [Von Neumann] began work in that field in 1927, the methods used by [quantum mechanics'] founders were hard to formulate in precise mathematical terms. . . . Von Neumann showed that mathematical rigor could be restored by taking as basic axioms the assumptions that the states of a physical system were points of a Hilbert space and that the measurable quantities were Hermitian (generally unbounded) operators densely defined in that space. This formalism, the practical use of which became available after von Neumann had developed the spectral theory of unbounded Hermitian operators (1929), has survived subsequent developments of quantum mechanics and is still the basis of nonrelativistic quantum theory" (DSB). In the introduction to this paper, Von Neumann stated that it was a continuation and extension of a 1934 paper by P. Jordan, E. Wigner and himself, published in the Ann. Math. under the same title. The offprint was published in Moscow in what was certainly a very small edition; this copy is of particular interest for its manuscript corrections in the author's hand, some of which amount to two or three sentences. Heims, John von Neumann and Norbert Weiner, pp. 100-115. See Mehra & Rechenberg, Hist. Dev. Quantum Theory, 3, pp. 122-23 (note). For an example of von Neumann's handwriting, see Aspray, John von Neumann and the Origins of Modern Computing, p. 231.